Chapter 8, Problem 1P

To determine

To plot:

The polynomial $y=0.5x^5-0.3x^4-15.5x^3+7x^2+36x-7$ in the domain $-4\le x\le 4$ by first creating a vector for $x$, next using the $\text{polyval}$ function to calculate $y$, and then using the $\text{plot}$ function.

Answer to Problem 1P

Solution:

The plot of the given polynomial $y=0.5x^5-0.3x^4-15.5x^3+7x^2+36x-7$ is stated as follows.

Explanation of Solution

The given polynomial function is,

$y=0.5x^5-0.3x^4-15.5x^3+7x^2+36x-7$ ............. (1)

The range of function is $-4\le x\le 4$.

Substitute the value of $x=-4$ in the above equation.

$\begin{array}{c}y=0.5x^5-0.3x^4-15.5x^3+7x^2+36x-7\\ =0.5{\left(-4\right)}^5-0.3{\left(-4\right)}^4-15.5{\left(-4\right)}^3+7{\left(-4\right)}^2+36\left(-4\right)-7\\ =-45.4\end{array}$

Substitute the value of $x=-4$ in equation (1).

$\begin{array}{c}y=0.5x^5-0.3x^4-15.5x^3+7x^2+36x-7\\ =0.5{\left(4\right)}^5-0.3{\left(4\right)}^4-15.5{\left(4\right)}^3+7{\left(4\right)}^2+36\left(4\right)-7\\ =101.80\end{array}$

Hence, the value of $y$ lies from $-45.4\le y\le 101.8$.

Write the MATLAB script to plot the polynomial $y=0.5x^5-0.3x^4-15.5x^3+7x^2+36x-7$ in the domain $-4\le x\le 4$ by first creating a vector for $x$, next using the $\text{polyval}$ function to calculate $y$, and then using the $\text{plot}$ function.

MATLAB Code:

%MATLAB program to plot the polynomial function

x = -4:0.1:4;%Define a vector x.

y = [0.9 -0.3 -15.5 7 36 -7];

r = polyval(y,x);%polyval function is used to calculate y

plot(x,r)

Save the MATLAB script with name, Chapter8_56830_8_1P.m in the current folder. Execute the script by typing the script name at the command window to get the plot of the polynomial $y=0.5x^5-0.3x^4-15.5x^3+7x^2+36x-7$ in the domain $-4\le x\le 4$ by first creating a vector for $x$, next using the $\text{polyval}$ function to calculate $y$, and then using the $\text{plot}$ function.

Result:

Conclusion:

Therefore, the plot of the given polynomial $y=0.5x^5-0.3x^4-15.5x^3+7x^2+36x-7$ is stated above.